Currently (to my knowledge), it is not possible to see any lotting attempts until an item drops (at which point it's too late to do anything about it).

It would seem that the developers have made a design choice to keep people from seeing what others have lotted, and I can understand (if not necessarily agree with) the reasons behind hiding lot values until the item drops.

However, I think an acceptable compromise would be to display a notification for the type of lot a player has cast as they cast it. For example:

Player A has cast Greed on the Heavy Allagan Armor.
Player B has cast Need on the Vortex Ring of Healing.
Player C has cast Pass on the Wave Harpoon.

This would help identify both "accidental" lots and "ninja" lots before it is too late to do anything about it, with minimal exposure to the potential gamesmanship of high/low counterlotting (e.g. I only lot if someone else in the party lotted higher than my friend).